Metastability in the two-dimensional Ising model with free boundary conditions

TL;DR

This paper analyzes the metastability phenomenon in the 2D Ising model with free boundary conditions, focusing on nucleation processes and lifetime estimation at low temperatures, combining analytical and simulation methods.

Contribution

It provides an analytical computation of metastable phase lifetime and identifies nucleation at corners as the exit mechanism, extending understanding of boundary effects in magnetic systems.

Findings

Metastable phase lifetime is analytically derived at low temperatures.

Nucleation occurs predominantly at system corners.

Monte Carlo simulations confirm analytical results.

Abstract

We investigate metastability in the two dimensional Ising model in a square with free boundary conditions at low temperatures. Starting with all spins down in a small positive magnetic field, we show that the exit from this metastable phase occurs via the nucleation of a critical droplet in one of the four corners of the system. We compute the lifetime of the metastable phase analytically in the limit $T\to 0$, $h\to 0$ and via Monte Carlo simulations at fixed values of $T$ and $h$ and find good agreement. This system models the effects of boundary domains in magnetic storage systems exiting from a metastable phase when a small external field is applied.